MELBOURNE — The future of 80-year-old Goldfield Corp. appears to be hanging precariously on the company's efforts to sell a money-losing silver mine in New Mexico.

John H. Sottile, the 38-year-old president and chief executive officer of the Melbourne-based company, concedes the seriousness of Goldfield's current dilemma. But his company, today a holding corporation for mining and electrical construction businesses, has survived more threatening times, he said.

Indeed, Goldfield's financial record is, if nothing else, an indicator of corporate grit. Since 1965, the publicly held company has reported a profit in only six years.

There were some high-rolling days in the late '60s, when Goldfield held offices on Fifth Avenue in New York and when its vision of profitability went far beyond mining.

The Sottile family of Brevard County bought into the business in 1969, exchanging 28,000 acres of Florida real estate and citrus groves for Goldfield stock. Little Goldfield then seemed on the verge of greatness; the Sottiles instead met disaster.

At the time, Goldfield owned the controlling share of the convenience food and tourism giant, the $151 million-a-year General Host Corp. General Host had a substantial interest in the Armour Corp. and its strategy, investors knew, was to acquire control of Armour, Sottile said.

When Greyhound Corp., however, entered the battle for Armour, General Host's plan fell through, according to the company's 1969 annual report. Then, through a complex corporate maneuver, General Host managed to repossess all of Goldfield's General Host stock, which had been pledged to an $11 million loan on behalf of General Host.

Several years of litigation ensued, and Goldfield eventually received a settlement of ''several million and properties,'' Sottile said. But the sum was not equal to what it lost, he said. The company had been left in the interim with undeveloped mining properties and no capital to explore them.

''It was through the tenacity of my father (James Sottile Jr., now board chairman) that it did not go bankrupt,'' said Sottile, who assumed leadership of the company in 1983 following the death of his brother, James III. ''I assure you it was sheer will that kept it going.''

The sale of the company's real estate for $10 million in 1972 was part of the company's rescue. Goldfield went on to develop other mining properties, but true to its tradition, remained much more than a mining company.

''We try to avail ourselves of opportunities,'' Sottile said.

The company purchased Tropicana Pools Inc. of Orlando in 1974 for $4 million and sold it in 1978 for $1.9 million after several years of losses. Tropicana, which finally collapsed in 1979, left at least 230 uncompleted swimming pools and a storm of controversy in its wake.

Goldfield's past is admittedly ''colorful,'' Sottile said, but today the company is walking a more conservative line. Most recent losses are a result of market forces. Its strategy for survival is one that has seemed to work in the past. ''If you have an unprofitable business, you get rid of it,'' Sottile said.

In 1985, Goldfield reported a loss of $3.6 million -- much of it depreciation and write-offs -- on revenue of $4.3 million. The company's independent public accountants, Peat, Marwick, Mitchell and Co., questioned Goldfield's ability to continue as a going concern, pointing to such problems as two consecutive years of multimillion dollar losses and its $2.2 million excess of currrent liabilities over current assets. Goldfield must pay $3.3 million on a bank credit agreement with Continental Illinois Bank by July 1.

Sunshine Mining Co., a $65 million-a-year Dallas-based company, has bought an option that expires June 1 on Goldfield's St. Cloud Silver Mine in New Mexico. If the option is exercised, Goldfield would be paid with Sunshine common stock valued at $5.1 million.

The St. Cloud mine is Goldfield's big dream turned nightmare. The company discovered the high-grade silver ore mine in 1968. When silver prices started up in 1979 the company began exploration and development. The company pumped between $10 million and $13 million into the project.

In 1980, the company's mine even won the interest of Dallas multimillionaire Nelson Bunker Hunt. Hunt was to purchase 1 million shares of Goldfield stock and buy a 20 percent interest in the mine for $2 million with a four-year option for additional ownership. That deal fizzled.

''Mr. Hunt became embroiled in other problems,'' Sottile said.

It was Hunt, of course, who attempted to corner the silver market in 1980 and sent prices soaring to as high as $48 an ounce, said John Lutley, executive director of the Washington, D.C.-based Silver Institute.